Question: Simplify the following expression: $y = \dfrac{5q^2 - 75q + 270}{q - 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ y =\dfrac{5(q^2 - 15q + 54)}{q - 6} $ Then we factor the remaining polynomial: $q^2 {-15}q + {54} $ ${-6} {-9} = {-15}$ ${-6} \times {-9} = {54}$ $ (q {-6}) (q {-9}) $ This gives us a factored expression: $\dfrac{5(q {-6}) (q {-9})}{q - 6}$ We can divide the numerator and denominator by $(q + 6)$ on condition that $q \neq 6$ Therefore $y = 5(q - 9); q \neq 6$